Problem: Solve for $x$ : $7\sqrt{x} - 6 = 4\sqrt{x} + 5$
Subtract $4\sqrt{x}$ from both sides: $(7\sqrt{x} - 6) - 4\sqrt{x} = (4\sqrt{x} + 5) - 4\sqrt{x}$ $3\sqrt{x} - 6 = 5$ Add $6$ to both sides: $(3\sqrt{x} - 6) + 6 = 5 + 6$ $3\sqrt{x} = 11$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{11}{3}$ Simplify. $\sqrt{x} = \dfrac{11}{3}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{11}{3} \cdot \dfrac{11}{3}$ $x = \dfrac{121}{9}$